-Documentation of widespread cospeciation in a host-parasite assemblage requires statistical evidence that the congruence observed between the host and parasite phylogenies exceeds that expected by chance. Although the validity of this test rests on the assumption of independence of the host and parasite phylogenies, this critical assumption may be violated in many tests of cospeciation. Herein, we emphasize the need for rigorous tests of cospeciation in host-parasite assemblages, and we show how estimates of genetic distance can be used to investigate relative rates of evolution and timing of phylogenesis in the hosts and parasites once widespread cospeciation has been documented for the assemblage. The method involves a nonparametric test of association between genetic-distance matrices for the hosts and their parasites. If the association is statistically significant, the relationship is examined in greater detail using bivariate analysis. We use an example from our studies of pocket gophers and chewing lice to illustrate how genetic distances can be used to explore relative rates of genetic change in the two groups and to investigate relative timing of cospeciation events in the assemblage. [Cospeciation; host-parasite coevolution; rates of evolution; genetic distances; pocket gophers; chewing lice.] Within the broad context of host-parasite coevolutionary theory, the inference of cospeciation is considered appropriate for a given host-parasite assemblage if the hosts and their parasites show identical patterns of phylogenetic differentiation. In practice, however, identical patterns of phylogenesis in hosts and their parasites are only rarely observed. Thus, in most studies of cospeciation, the investigator must accept a certain degree of discordance between host and parasite phylogenies and ask whether evidence of cospeciation is widespread within the assemblage. The search for widespread cospeciation usually involves a general assessment of congruence between host and parasite phylogenies or between host and parasite taxonomic boundaries or geographic distributions (e.g., Kethley and Johnston, 1975; Kim et al., 1975; Eveleigh and Amano, 1977; Brooks, 1979; Fain, 1979; Moss, 1979; 1 Present address: Department of Biological Sciences, Northern Illinois University, DeKalb, Illinois 60115. Radovsky, 1979; Hellenthal and Price, 1984). In comparisons of host and parasite genealogical trees, the inference of widespread cospeciation usually involves subjective appraisal of branching similarity, wherein a high level of congruence is assumed to reflect widespread cospeciation of hosts and their parasites, and a low level of congruence indicates that the majority of observed host-parasite associations cannot be attributed to parallel phylogenesis. Until recently (Humphries et al., 1986; Brooks, 1987; Simberloff, 1987; Page, 1989, 1990), few workers have quantified similarity between host and parasite phylogenies. Because the inference of widespread cospeciation is unwarranted if the observed similarity can be explained by chance, it is critical that investigations of cospeciation include assessments of the statistical significance of topological similarity of host and parasite phylogenetic trees. Even more fundamental to documentation of cospeciation is the logical and statistical requirement for independence of
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